The present invention generally relates to an apparatus for positioning and orienting a member in space and to joints for linking limbs of such an apparatus.
A need exists for simple and effective parallel kinematics mechanisms. Kinematics mechanisms are used in mechanical engineering applications for machining, robotics, positioning devices, coordinate measuring, fixtures and so on. In general, mechanisms can typically be classified as either serial or parallel. Serial kinematics mechanisms are widely used and presently dominate the market.
A serial kinematics mechanism has a series of cantilever beams that are movably connected together in an end-to-end fashion by prismatic, revolute or spherical joints, forming an open loop. The closer that a member is to a base of the mechanism within the serial structure, the higher the load on that member. Additionally, the farther that a member is from the base, the higher its deflection with respect to the base member. When a serial kinematics mechanism is subjected to loading, the position of the farthest member, i.e., the end-effector, is subject to the cumulative deflections of all serial members. Unfortunately, this results in large positioning errors at the end-effector. Being constructed of cantilevers, a serial mechanism has a poor stiffness to mass ratio, making such structures bulky in design.
Serial kinematics mechanisms allow fast and easy computation of the position of the end-effector given the position or state of all actuators. In general, this computation is known as the forward kinematics of a mechanism. However, determining the position or state of all actuators given the position of the end-effector, also known as the inverse kinematics, is very difficult.
Relative to serial kinematics mechanisms, parallel kinematics mechanisms typically have an improved stiffness-to-mass ratio and better accuracy. A parallel kinematics mechanism has a plurality of links which form one or more closed loops, the links thereby sharing the load on the end-effector. Moreover, positioning errors of actuators are divided, thereby resulting in a high accuracy of the end-effector. A well-known parallel kinematics mechanism is the Stewart Platform which was introduced in 1965 and has since been the subject of extensive study and analysis. A Stewart Platform mechanism generally includes a movable platform which is connected to a base by six controllable links. For example, U.S. Pat. No. 5,656,905 discloses a general overview on mechanisms that are based on or derived from the Stewart Platform.
While parallel kinematics mechanisms can provide improved accuracy, stiffness, and high load carrying capacity, parallel mechanisms also suffer from significant control drawbacks. Most known parallel kinematics mechanisms have very difficult forward kinematics. The solutions of the forward kinematics are in the form of high-order polynomial equations, which do not allow closed-form solutions to compute the end-effector position. Computationally intensive methods such as numerical approximations must be applied in order to calculate multiple solutions and select the right one. In some cases, particularly in lower degree of freedom mechanisms, closed-form solutions may exist. However, these solutions involve algebraically complex expressions with fractional powers. Moreover, many of the aforementioned parallel kinematics mechanisms require run-time collision detection between their parallel members, further complicating the control calculations.
It has been shown that the general form of the Stewart Platform has forty feasible solutions. For some special forms of the Stewart Platform, closed-form solutions of forward kinematics exist. In these special forms, pairs of spherical joints that connect the links to base and platform are concentric. However, the difficulty of manufacturing such joints is well recognized in the art.
Some efforts have been made by designing ball and socket joints, which allow two or more links to be connected to the platform or base with independent spherical motion about a common point. However, these joints significantly restrict the range of spherical motion of the attached links and have a limited load carrying capacity. Moreover, fabrication of such a joint is very expensive and difficult.
Parallel kinematics mechanisms are increasingly used in machining and robotics. Several mechanisms for free-form milling have been introduced into the market recently. Most of the known mechanisms are based on the Stewart Platform and allow all six degrees of freedom. These known Stewart Platform mechanisms have limited the translational and rotational motion of the end-effector. However, many applications such as machining or assembly operations require actuation about one rotational axis with infinite or very high freedom, which is usually accomplished by motors or spindles mounted on the end-effector. This means that one of the actuations of these mechanisms is redundant. Because of their particular configuration, many of the aforementioned parallel kinematics mechanisms require run-time collision detection between their parallel members. Further, most known parallel kinematics mechanisms have complex polyhedral workspaces whereas engineering applications generally require cuboidal workspace shapes. This leads to a poor workspace utilization ratio for many parallel kinematics mechanisms.
A need therefore exists to provide a parallel kinematics mechanism that has simple and practical forward kinematics solutions by allowing the solution for the end-effector position in closed-form. A need exists for such a mechanism that has a robust and modular design with no redundant actuators and joints.
Moreover, a need exists to provide a rigid and accurate mechanism with large translational and rotational motion range in a cuboidal workspace. Ideally, stiffness and accuracy properties throughout the workspace of the mechanism should remain constant. The configuration of the mechanism should inherently prevent collision between its parallel members.
The present invention also relates to mechanical joints, and more particularly, to spherical joints used to allow spherical motion to three or mote limbs about a common point.
A variety of mechanical joints are known which allow spherical motion for multiple limbs about a common point. Some such joints are constructed by three hemispherical shells concentrically mounted on a ball, representing an extension of a ball and socket joint. Such a joint is disclosed, for example, in U.S. Pat. No. 5,179,525. The shortcoming of this type of joint is that the spherical motion of each limb becomes increasingly limited the greater the number of limbs connected to the ball. The joint does not allow tensile loads or high forces in general and suffers from poor rigidity and accuracy. Control of structures having such a joint, becomes difficult due to the non-linear nature of the high frictional forces produced by the preloaded ball and socket assemblies. Moreover, it is not possible to access the center of the joint without restricting spherical motion of the limbs. Neither can the joint be stacked to increase the number of interconnected limbs while maintaining concentricity.
Another joint has been made using extra yokes on a universal joint assembly, as disclosed, for example, in U.S. Pat. No. 5,797,191 and E. Fichter, A Stewart Platform-Based Manipulator: General Theory and Practical Construction, 1986, The International Journal on Robotics Research, Vol. 5, pp. 157-182. The mechanism allows only limited spherical motion and involves redundant revolute joints. Due to its asymmetric design, the joint suffers singularities in certain configurations. Furthermore, it cannot be stacked to increase the number of interconnected limbs and does not allow access to the center of the joint.
Another known joint as disclosed in U.S. Pat. No. 5,657,584, uses a large number of elements and pins to produce spherical motion of the attached limbs. Although this type of joint can be stacked to increase the number of interconnected limbs and allows access to the center point, it requires multiple expensive revolute joints and a complex structure. Consequently, such joint is not capable of carrying high loads and offers only limited spherical motion to its limbs.
In some joints, the limbs are not truly independent to rotate about each other, as it should ideally be for a concentric spherical joint. They are constrained with spatial relationships. For example, the members must move on a conical surface.
In other joints, the centers of rotation of the attached limbs are not coincident. This may cause at least two problems. Firstly, compressive and tensile loads in the limbs cause twisting and bending moments on the joint, and the loads are not transmitted to the other limbs as in an ideal truss. Secondly, in a controlled truss structure such as parallel kinematics machines, this kind of joint results in difficult forward kinematics that allow no closed-form solution of the end-effector position in general.
A need therefore exists for a joint structure that has improved spherical motion about a point common to its interconnected limbs than previously known joints. The joint should allow any configuration of its limbs with none of the limbs hindering the motion of any other.
The present invention provides a parallel kinematics mechanism which overcomes difficulties incurred in prior art devices. The invention further includes an improved joint structure which facilitates the construction of such an improved kinematics mechanism by allowing three or more axes to intersect at a point, regardless of their orientation.
An object of the invention is to provide an improved mechanism for positioning and orienting a member in space. A more specific object of the invention is to provide such a mechanism which facilitates simplified forward kinematics calculation with a closed-form solution. Yet another object is to provide such a mechanism with improved structural rigidity.
Advantageously, a kinematics mechanism having a design according to the present invention is such that the forward kinematics math is greatly simplified. The design of the proposed mechanism reduces calculations to the simple problem of finding the point of intersection of three spheres, which makes the forward kinematics trivial and has a closed-form solution for the end-effector position. The closed-form solution only involves simple algebraic expressions. According to an embodiment of the invention, the solution simplification has been achieved by a new concentric spherical joint that allows three or more limbs to be connected together with their longitudinal axes always intersecting at a point, regardless of the orientations.
In an embodiment, the invention utilizes a concentric spherical joint such that the structure of the positioning mechanism resembles a bi-tetrahedral configuration, giving it truss-like behavior. The bi-tetrahedral arrangement also causes decoupling between the position and orientation of the final member. Loads on the end-effector are generally distributed among all actuators which, in return, compensate for positioning errors of the end-effector through their parallel arrangement. Thereby, the mechanism provides high stiffness and accuracy. Due to the bi-tetrahedral configuration, no collision detection between parallel members is required.
Another advantage of the configuration is the high workspace volume the end-effector can reach, combined with a high dexterity throughout this workspace which is nearly cubical in shape. Furthermore, the positioning mechanism is able to operate at high speeds due to its parallel design and simple closed-form solution.
Work tools such as cutting tools or robot grippers can be mounted on the end-effector. In an embodiment, the work tool is powered by an actuator or a motor that is fixed on the base and transmits its rotation on the work tool through a telescopic spline-shaft assembly. This allows moments acting about the longitudinal axis of the working member to be directly transferred to the base, relieving the overall structure of the positioning mechanism. In another embodiment, the work tool is powered by an actuator or a motor that is fixed on the end component.
Another advantage of the invention is that, in an embodiment, it provides a mechanism that fixedly has a modular design that only uses five identical actuator assemblies, two kinds of concentric spherical joints, a base, a motor, and a working member. The low number of parts and the usage of mostly revolute joints results in a precise and cost-efficient positioning mechanism that finds wide use in many areas.
Mechanisms according to an embodiment of the invention may be useful in machining and robotics. In particular, the mechanism can be used for free-form milling, assembly operations, and coordinate measuring or any other kind of operation that requires a member to be positioned and oriented in space.
In an embodiment, another object of the invention is to provide a concentric spherical joint that allows three or more limbs to be connected together with their longitudinal axes always intersecting at a point, regardless of their orientation. This joint provides advantages over the prior art, exhibiting an improved range of spherical motion among its joined limbs, few parts, low wear and friction, improved rigidity, and improved accuracy. It also can sustain tensile loads, unlike some ball-and-socket joints. The proposed concentric spherical joint according to an embodiment of the invention advantageously has a simple and robust design, involving only a minimum number of required revolute joints, providing total spherical motion to three interconnected limbs.
A structure can be assembled using several concentric spherical joints according to an embodiment of the invention to increase the number of limbs to any number with their longitudinal axes intersecting at a common point. While combinations of known joints constrain the spherical motion range, the concentric spherical joint according to an embodiment of the invention enhances this range.
The concentric spherical joint according to an embodiment of the invention has many applications in a wide range of engineering disciplines. It may be used in civil engineering for spatial trusses, space grid structures, and geodesics. When used as a joint in a parallel kinematics mechanism, the concentric spherical joint can extremely simplify the forward kinematics and reduce the amount of necessary computations, allowing a parallel kinematics mechanism to operate at significantly higher speeds.